> **SUPERSEDED.** This file was published for about an hour on 7 September 2026 and is superseded by the version above. Its notes carry the date **9 September 2026**, which was the date on the desk's draft and not the date the notes were appended. The ruling is explicit — *the date on each note is the date WC appends it* — and that date is 7 September 2026. Two of its notes also predate G's ruling on their text: AP30's item 10 did not carry C beside R, its item 11 did not carry the sentence on the now, and AP49's note did not carry the §0.2 pointer. It is kept, never deleted, because it was published: it is in Zenodo version 10.5281/zenodo.22646076, which is permanent.

---

# Republish AP47 — FINAL v3 · dated note 9 September 2026

The locked body is untouched. The notes are appended after the section that closes the argument, which is where AP30's first five sit. Verified after the build: the source of record placed beside this note reproduces the new PDF paragraph for paragraph, and **every body sentence of the previous PDF is present in the new one** — 0 lost, checked sentence by sentence.

One further change, in the front matter only: the Contents entry for **6 — The Application, Once** read page 12. That heading is on page 11, and was on page 11 in the previous PDF too — the typed number was wrong before this republish. Word's own pagination now supplies 11. Dress, not body.

## The two published files, both kept

*Beside, never replaced* applies to the rendered PDF as well as the text.

| | file | sha256 | pages |
|---|---|---|---|
| **published 4 September – 8 September 2026 (no notes)** | `proofs/instruments/AP47/AP47_The_Flip_FINAL_v3_published_to_2026-09-08.pdf` | `cccf073de1368e8a6e4a1a4636d2f8c7167827857960b19d7cb04461a30a3e3b` | 16 |
| **published from 9 Sep 2026** | `/AP47_The_Flip.pdf` | `c0be5d61157b6ddb8f076ef266c3ad6e0f048d000f245228e10e9755d296893b` | 17 |

**The outgoing digest is cited by:** `proofs/instruments/AP47/SOURCE_OF_RECORD.md` — frozen files, not edited. The digest they cite resolves to the preserved file above, which is why it is kept at a stable path and not only in git history.

## The notes, for the record

> 9 September 2026. Two matters of record. Nothing in the body is altered.
>
> 1. The second-order correction written in §5 as a divisor, Δ_bare/(1 + α²/8π), reads as the multiplier, Δ_bare·(1 − α²/8π): the isotropic-leakage lemma has one form everywhere in the corpus, because a returned leak is not an expression and does not itself leak (AP30 dated note 9; AP49 §4). At this paper's precision the two differ by 4.5 × 10⁻¹²; no digit moves.
>
> 2. §5's retirement of the identification of the four dimensions with the four conditions applies to this paper's derivation chain, which did not need it; it is not a ruling against AP10, which identifies each of the four axioms with one face of the manifold.
>

Ruled by G, 9 September 2026, on the desk's replies of 8 September (`museum/desk/AP30_first_replies_2026-09-08_v2.md`).

*A locked body is never edited, replaced or removed — corrections go beside it by dated note. A lemma that must be rewritten becomes v2.0 with v1.0 kept beside it.*